Starting control apparatus for internal combustion engine

When a first motor MG1 cranks and starts an engine 150 that is in the cold, the revolving speed of the engine does not increase quickly 150. It is accordingly required to control the first motor MG1, in order to prevent electric power 194 stored in a battery from being wasted. A starting control apparatus does not cause the first motor MG1 to output a torque corresponding to a difference between a target revolving speed N* and an actual revolving speed Ne of the engine 150, but gradually increases a target torque STG by the open-loop control and restricts the magnitude of the target torque STG to a preset maximum torque STGMAX, which depends upon a cooling water temperature Tw of the engine 150. When the engine 150 is in the cold, the high viscosity of lubricant causes the revolving speed of the engine 150 not to quickly increase in response to the high target torque set to the first motor MG1. In this case, the maximum of the target torque is restricted to a smaller value, so as to prevent the electric power stored in the battery 194 from being wasted. The injection allowable revolving speed, at which the fuel injection to the engine 150 is allowed to start, is also set equal to a small value. This causes the engine 150 to start self driving at an earlier timing, thereby saving the electric power consumed by the first motor MG1.